Assembling approximately optimal binary search trees efficiently using arithmetics

We introduce a new algorithm for computing an approximately optimal binary search tree with known access probabilities or weights on items. The algorithm is simple to implement and it has two contributions. First, a randomized variant of the algorithm produces a binary search tree with expected perf...

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Veröffentlicht in:Information processing letters Jg. 109; H. 16; S. 962 - 966
1. Verfasser: Kujala, Jussi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 31.07.2009
Elsevier
Elsevier Sequoia S.A
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Approximation algorithms
Binary search trees
Binary system
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Data processing. List processing. Character string processing
Data structures
Entropy
Entropy bounds
Exact sciences and technology
Graph theory
i/o cost models
Information processing
Mathematics
Memory organisation. Data processing
Miscellaneous
Probability
Random variables
Sciences and techniques of general use
Software
Studies
Theoretical computing
Binary search trees
Data structures
Approximation algorithms
Entropy bounds
i/o cost models
Costs
Arithmetics
Node
I/O cost models
Entropy
Probability distribution
Approximation algorithm
Computing
Implementation
Input
Distribution function
Data structure
Random variable
Approximation
Computer theory
Probability
Search algorithm
Upper bound
Binary tree
Binary search tree
Distribution
Information processing
Search tree
Expectation
Performance
Algorithm analysis
ISSN:0020-0190, 1872-6119
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Zusammenfassung:We introduce a new algorithm for computing an approximately optimal binary search tree with known access probabilities or weights on items. The algorithm is simple to implement and it has two contributions. First, a randomized variant of the algorithm produces a binary search tree with expected performance that improves the previous theoretical guarantees (the performance is dependent on the value of the input random variable). More precisely, if p is the probability of accessing an item, then under expectation the item is found after searching lg 1 / p + 0.087 + lg 2 ( 1 + p max ) nodes, where p max is the maximal probability among items. The previous best bound was lg 1 / p + 1 , albeit deterministic. For the optimal tree our upper bound implies a non-constructive performance bound of H + 0.087 + lg 2 ( 1 + p max ) , where H is the entropy on the item distribution and the previous bound was H + 1 . The second contribution of the algorithm is a low cost in i/o models of cost such as the cache-oblivious model, while attaining simultaneously the above bound for the produced tree.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2008.08.012